Group #13130142 — subgroups

Subgroups — #13130142

Order 1664.

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11719421	C₂	1	1	yes	maximal, characteristic
2	#11719051	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₃⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄⋊#1057	C₂	1	4	yes	maximal, complemented
5	C₂×#6129	—	2	1	no	—
6	C₂×D₁₃⋊C₈	—	2	1	no	—
7	C₁₃×#127	C₄	1	1	yes	characteristic
8	#88192	—	2	1	no	—
9	#88192	C₄	1	2	yes	—
10	#88190	—	2	1	no	—
11	D₄×Dic₁₃	—	2	1	no	—
12	D₄×Dic₁₃	C₂²	1	2	yes	—
13	C₄²×D₁₃	C₂²	1	1	yes	characteristic
14	#88123	C₄	1	1	yes	characteristic
15	#88112	—	2	1	no	—
16	#88111	—	2	1	no	—
17	C₄⋊#1057	—	2	1	no	—
18	C₄⋊#1057	C₂²	1	2	yes	—
19	C₄×#1057	C₂²	1	2	yes	—
20	C₂×D₄×C₁₃	—	2	1	no	—
21	C₂×D₄×C₁₃	—	2	1	no	—
22	C₂×D₄×C₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₂²⋊D₁₃	—	2	2	no	—
24	C₂²×Dic₁₃	—	2	2	no	—
25	#6129	—	4	2	no	—
26	#6129	—	4	2	no	—
27	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
29	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
30	C₂×Dic₂₆	—	2	1	no	—
31	C₂×#1057	—	2	2	no	—
32	C₂×#1057	—	2	2	no	—
33	D₁₃⋊C₈	—	4	2	no	—
34	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²⋊Dic₁₃	—	2	2	no	—
36	C₂²⋊Dic₁₃	—	2	2	no	—
37	C₄⋊Dic₁₃	—	2	1	no	—
38	C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
39	C₄×Dic₁₃	D₄	1	1	yes	characteristic
40	C₄×Dic₁₃	D₄	1	1	yes	characteristic
41	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
42	#1480	—	13	1	no	maximal, Sylow
43	C₂³×C₁₃	—	2	2	no	—
44	C₂²×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
45	D₄×C₁₃	—	2	4	no	—
46	D₄×C₁₃	—	4	2	no	—
47	D₄×C₁₃	—	4	2	no	—
48	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂²⋊D₁₃	—	4	4	no	—
52	C₂×Dic₁₃	—	2	2	no	—
53	C₂×Dic₁₃	—	4	2	no	—
54	C₂×Dic₁₃	—	4	2	no	—
55	C₂×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
58	C₄×D₁₃	—	2	2	no	—
59	C₄×D₁₃	—	4	1	no	—
60	C₄×D₁₃	D₈	1	2	yes	—
61	C₄×D₁₃	SD₁₆	1	2	yes	—
62	Dic₂₆	—	4	2	no	—
63	#1057	—	4	2	no	—
64	#1057	—	4	2	no	—
65	#532	—	13	1	no	—
66	#431	—	13	1	no	—
67	C₂×C₄⋊C₈	—	13	1	no	—
68	D₄⋊C₈	—	13	4	no	—
69	C₂²×C₁₃	—	4	2	no	—
70	C₂²×C₁₃	—	4	2	no	—
71	C₂²×C₁₃	—	4	2	no	—
72	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×D₁₃	—	2	1	no	—
74	C₂×D₁₃	—	2	1	no	—
75	C₂×D₁₃	#102	1	2	yes	—
76	C₄×C₁₃	—	2	1	no	—
77	C₄×C₁₃	#102	1	2	yes	—
78	C₄×C₁₃	#131	1	2	yes	—
79	Dic₁₃	—	2	1	no	—
80	Dic₁₃	—	2	1	no	—
81	Dic₁₃	—	4	2	no	—
82	Dic₁₃	C₂×D₈	1	1	yes	characteristic
83	Dic₁₃	C₂×SD₁₆	1	1	yes	characteristic
84	C₂×#41	—	26	1	no	—
85	C₂²×C₈	—	26	1	no	—
86	C₄⋊Q₈	—	13	1	no	—
87	#127	#261	1	1	yes	characteristic
88	#124	—	26	1	no	—
89	#121	—	13	2	no	—
90	#121	—	26	1	no	—
91	C₄×D₄	—	13	2	no	—
92	C₄×D₄	—	26	1	no	—
93	C₂×C₄²	—	13	1	no	—
94	C₄⋊C₈	—	13	2	no	—
95	C₄⋊C₈	—	26	1	no	—
96	C₄⋊C₈	—	26	1	no	—
97	C₂²⋊C₈	—	26	1	no	—
98	C₄×C₈	—	13	2	no	—
99	C₂×C₁₃	—	8	2	no	—
100	C₂×C₁₃	#408	1	1	yes	characteristic
101	C₂×C₁₃	C₂×#102	1	1	yes	characteristic
102	C₂×C₁₃	#421	1	1	yes	characteristic
103	D₁₃	—	2	2	no	—
104	#41	—	52	2	no	—
105	#41	—	52	2	no	—
106	C₂×Q₈	—	26	1	no	—
107	C₂×D₄	—	2	1	no	—
108	C₂×D₄	—	2	1	no	—
109	C₂×D₄	—	26	2	no	—
110	C₂×D₄	C₂×#261	1	2	yes	—
111	C₂²×C₄	—	13	1	no	—
112	C₂²×C₄	—	13	1	no	—
113	C₂²×C₄	—	13	1	no	—
114	C₂²×C₄	—	26	2	no	—
115	C₂×C₈	—	26	2	no	—
116	C₂×C₈	—	26	2	no	—
117	C₂×C₈	—	52	2	no	—
118	C₄⋊C₄	—	13	2	no	—
119	C₄⋊C₄	—	26	1	no	—
120	C₂²⋊C₄	—	26	2	no	—
121	C₂²⋊C₄	—	26	2	no	—
122	C₄²	—	13	1	no	—
123	C₄²	—	13	1	no	—
124	C₄²	—	13	1	no	—
125	C₄²	C₂×#261	1	1	yes	characteristic
126	C₁₃	#1480	1	1	yes	characteristic, complemented, Sylow
127	C₂³	—	2	2	no	—
128	C₂³	—	13	1	no	—
129	Q₈	—	52	2	no	—
130	D₄	—	2	4	no	—
131	D₄	—	4	2	no	—
132	D₄	—	4	2	no	—
133	D₄	—	52	4	no	—
134	C₂×C₄	—	13	1	no	—
135	C₂×C₄	—	13	2	no	—
136	C₂×C₄	—	13	2	no	—
137	C₂×C₄	—	13	1	no	—
138	C₂×C₄	—	13	1	no	—
139	C₂×C₄	—	26	2	no	—
140	C₂×C₄	—	26	2	no	—
141	C₂×C₄	—	52	1	no	—
142	C₂×C₄	—	52	2	no	—
143	C₂×C₄	—	52	2	no	—
144	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
145	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
146	C₂×C₄	C₂²×#261	1	1	yes	characteristic
147	C₈	—	52	2	no	—
148	C₈	—	52	2	no	—
149	C₂²	—	4	2	no	—
150	C₂²	—	4	2	no	—
151	C₂²	—	4	2	no	—
152	C₂²	—	13	2	no	—
153	C₂²	—	26	1	no	—
154	C₂²	—	26	1	no	—
155	C₂²	C₂×C₂²⋊#261	1	1	yes	characteristic
156	C₄	—	2	1	no	—
157	C₄	—	13	1	no	—
158	C₄	—	13	1	no	—
159	C₄	—	26	1	no	—
160	C₄	—	26	1	no	—
161	C₄	—	52	2	no	—
162	C₄	#88115	1	2	yes	—
163	C₄	#88238	1	2	yes	—
164	C₂	—	8	2	no	—
165	C₂	—	26	2	no	—
166	C₂	C₂×#88115	1	1	yes	characteristic
167	C₂	#11719140	1	1	yes	characteristic
168	C₂	#11719147	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11719421

C₂

yes

maximal, characteristic

#11719051

C₂

yes

maximal, characteristic, complemented

D₁₃⋊(C₄⋊C₈)

C₂

yes

maximal, characteristic, complemented

D₄⋊#1057

C₂

yes

maximal, complemented

C₂×#6129

—

C₂×D₁₃⋊C₈

—

C₁₃×#127

C₄

yes

characteristic

#88192

—

#88192

C₄

yes

—

#88190

—

D₄×Dic₁₃

—

D₄×Dic₁₃

C₂²

yes

—

C₄²×D₁₃

C₂²

yes

characteristic

#88123

C₄

yes

—

—

—

C₂²

yes

—

C₄×#1057

C₂²

yes

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

C₂×C₄

yes

—

C₂×C₂²⋊D₁₃

—

C₂²×Dic₁₃

—

#6129

—

#6129

—

C₂×C₄×D₁₃

C₂×C₄

yes

characteristic

C₂×C₄×D₁₃

D₄

yes

characteristic

C₂×C₄×D₁₃

D₄

yes

characteristic

C₂×Dic₂₆

—

C₂×#1057

—

C₂×#1057

—

D₁₃⋊C₈

—

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂²⋊Dic₁₃

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

C₂×C₄

yes

—

C₄×Dic₁₃

D₄

yes

characteristic

C₄×Dic₁₃

D₄

yes

characteristic

C₄×Dic₁₃

C₂³

yes

characteristic

#1480

—

maximal, Sylow

C₂³×C₁₃

—

C₂²×D₁₃

C₂²⋊C₄

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²⋊D₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₃

C₂×D₄

yes

characteristic

C₂×Dic₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

D₈

yes

—

C₄×D₁₃

SD₁₆

yes

—

Dic₂₆

—

—

—

—

—

C₂×C₄⋊C₈

—

D₄⋊C₈

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

#102

yes

—

C₄×C₁₃

—

C₄×C₁₃

#102

yes

—

C₄×C₁₃

#131

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

C₂×D₈

yes

characteristic

Dic₁₃

C₂×SD₁₆

yes

characteristic

C₂×#41

—

C₂²×C₈

—

C₄⋊Q₈

—

yes

—

—

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₂×C₁₃

—

100

C₂×C₁₃

#408

yes

characteristic

101

C₂×C₁₃

C₂×#102

yes

characteristic

102

C₂×C₁₃

#421

yes

characteristic

103

D₁₃

—

104

#41

—

105

#41

—

106

C₂×Q₈

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

C₂×#261

yes

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₄²

—

123

C₄²

—

124

C₄²

—

125

C₄²

C₂×#261

yes

characteristic

126

C₁₃

#1480

yes

characteristic, complemented, Sylow

127

C₂³

—

128

C₂³

—

129

Q₈

—

130

D₄

—

131

D₄

—

132

D₄

—

133

D₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

C₂²⋊#261

yes

characteristic

145

C₂×C₄

C₂²⋊#261

yes

characteristic

146

C₂×C₄

C₂²×#261

yes

characteristic

147

C₈

—

148

C₈

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

C₂×C₂²⋊#261

yes

characteristic

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

#88115

yes

—

163

C₄

#88238

yes

—

164

C₂

—

165

C₂

—

166

C₂

C₂×#88115

yes

characteristic

167

C₂

#11719140

yes

characteristic

168

C₂

#11719147

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#127	C₄
socle	C₂²×C₁₃	C₂×C₂²⋊C₄
prime radical	#11719421	C₂
cosocle	C₄×Dic₁₃	C₂³
hypercenter	#127	#261
hypocenter	C₁₃	#1480
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

subgroup

G/H

center

C₂²

C₂×C₂²⋊#261

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#261

Fitting

C₁₃×#127

C₄

socle

C₂²×C₁₃

C₂×C₂²⋊C₄

prime radical

#11719421

C₂

cosocle

C₄×Dic₁₃

C₂³

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #127

N	H ≅ G/N	type
2. #11719051	C₂	semidirect
3. D₁₃⋊(C₄⋊C₈)	C₂	semidirect
4. D₄⋊#1057	C₂	semidirect
126. C₁₃	#1480	semidirect

H ≅ G/N

type

2. #11719051

C₂

semidirect

3. D₁₃⋊(C₄⋊C₈)

C₂

semidirect

4. D₄⋊#1057

C₂

semidirect

126. C₁₃

#1480

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11719421	2
#11719051	2
D₁₃⋊(C₄⋊C₈)	2
D₄⋊#1057	2
#1480	13

subgroup

index

D₁₃⋊(C₄⋊C₈)

Subgroups — #13130142

Conjugacy classes of subgroups

Complements

Maximal subgroups